It depends on the resource. They were recommending doing that sometimes here because it starts your city with bonus hammers which helps it build everything faster. (The OP's question) You can save 50 or more turns on build times for early buildings given terrain which is huge. It's not always the long-term potential you need to think about as every turn matters early too in speed games.
Recall that most early cities are small and growing most of their early life. If you settle on basic flat terrain and work growth tiles first for faster growth (generally recommended) in many grassland cities you literally have only 1 hammer to work with for a while so your buildings are snail slow (The OP's situation). But you can't work a hammer tile without giving up growth from your 3 food tiles. Eventually workers improving stuff like cows or bison gives you a few hammers but this takes time, and some growth tiles never give hammers (bananas & wheat).
Whereas, if you start on a few different terrain features you get an extra starting hammer or two for good early production of buildings (100-200% faster) and can still work all the 3+ food tiles. You usually give up a little bit of improvement potential later but it's often worth it to jump-start your city. Also as inthesomeday pointed out republic helps you build earlier buildings by giving every new city +1 starting hammer (so no city gets below 2 and some get 3-4) and 5% to buildings.
The rule to keep in mind is every city will have at least 2 food 1 production no matter what. If your base tile has more then 2 food, more then 1 production, or more then 0 gold, faith, culture, etc...it'll add the extra to the base tile. The resource you settle on is maintained as well so if you ever build a building in the future or have a religion that buffs it, it'll also get added to the base tile even after settling.
Favorites are:
Settle on hill: for fortification advantage, and 2 starting hammers, could mean 100% to production if terrain is pure food.
Settle on mining lux hill: extra hammer, instant lux connection, 2-3 extra gold
Settle on calendar luxury resource: 2 extra gold and instant lux connection
Settle on iron-plains or horse-plains: comes out same as hills, I am more hesitant to do this though as the tech to improve and get 3 production comes early and I prefer the 3 hammer, 1 food tile to work. It is an extra early hammer though if you want that.
Lastly, If there is no tile like the above ones, I typically pick the worst, central tile location.
Settle on snow, tundra, marsh, or desert: Isolated flat desert or tundra is perfect. All base tiles are "improved" to 2 food 1 production so in the case of tundra and desert you get 2-3 extra yield out of the tile early game and have more tiles to work later as your city grows. Settling flat desert or tundra locations is especially good with dance of aurora or desert folklore as the faith is also included in base tile and you couldn't work the tile you settled otherwise.
These settling strategies may not be significant for smaller cities that don't fully utilize their hexes but big ones from a tradition game it makes a difference as it'll mean a better extra tile to work when your city gets big. Don't move too far away from the optimal position to do this, but keep it in mind as you grid in your early cities and it'll improve them long-term.
The reason many people like to settle on calendar resources is they are hard to work, especially in plains as the food is poor and the production isn't good enough to justify it either. They give basically only gold even after improvement which, though nice, is not what cities need in the beginning. Also if your lux is desert incense it's always better to settle on it if it is near the optimal position as it gets buffed to food-neutral. You probably couldn't work it otherwise. If you settle on it though you get the gold in your base tile which is an extra early 2 gpt that you probably couldn't have gotten for a while anyway since you couldn't work the tile till you grew big, don't need calendar to connect it, and have happiness to keep building cities. It can mean faster expos if you are going liberty especially. Generally hill is the best deal though as you give up very little--even in the case of a mining lux just 1 hammer for most of the game after you mine it and you couldn't be working very many of those anyway as it'd slow your growth until late-game.
Some things you should never settle on imo:
Bananas: under jungle is always plains which already has the base 1 production. So you lose food by removing the jungle and in fact before granary settling on a banana tile gives you no bonus at all. Much better to settle somewhere else and work the banana. Later you also get 2 science from it too.
Iron/horse on grass or similar: Base yield is already 2 food 1 production. So you get no bonus and give up the improvement bonus of extra production. This is the same for all 2 food 1 production tiles. You only lose settling on them--prior granary at least. Also you give up building buffs for things like +1 production from all quarries, etc.
Deer: Deer in forest are 2 food 1 hammer, a very nice early workable tile with improvement potential. But if you settle on it you remove the forest. So you get no bonus for doing this on plains before granary. If it is a flat grassland you get a small bonus of 3 food from base tile but it is generally better to work it as you still get the extra food from doing so and then later get the improvement opportunity AND the chopping hammers from clearing the forest (if you choose).
Cows/Bison/Wheat: generally any food-boosting tile I avoid. You do get a 1 food bonus from the base tile but these are better to work as you still get the extra food and then get the opportunity to improve them for even more extra hammers or food.
Sheep hills: I personally never settle these. Settling on it or improving it and working it is both 2 food 2 production. Since settling on it does give the same yield as improving and working it some people do it anyway but I typically don't because there is no objective bonus to doing so. Only do it if it is the best possible spot for some reason. Otherwise you are just giving up the potential to work it later. Settling on a normal hill gives the same bonus and then you could be working the sheep too.
The best benefit comes from working food or food-neutral tiles and settling on heavy hammer/gold tiles for this reason. In all cases yes you give up a few points of yield doing this, but in many cases the benefit is greater from getting the early bonus. Usualy you don't have the extra food to be working poor food tiles for a while anyway so you give up very little settling on them early game but get free yields from them in the base tile. Think about this choice, especially if in an area with lots of food but poor production as your build times will be super-slow if you build on flat ground.
I hope this clears things up.
The absolute best tile to settle on for an early production boost is iron/hill. It gives 2 extra hammers (3 total and 4 with republic). It gives a bit more later if you don't settle on it, but it takes a while to get the extra food to work an iron-hill so I think the +3-4 base hammers is a better deal. You'll speed through early build order in that city. The most powerful base tile for production is Russia, liberty, iron-hill for a bonus of 5 hammers.
Here's a discussion of the pros/cons of settling on resources:
http://gaming.stackexchange.com/que...-i-get-from-the-tile-on-which-i-place-my-city