Damn. I just realized I missed the entire backend of this thread.
Phonetically similar can have a number of different contexts, but generally it refers to sounds which bear similarities.
Consonants have 3 areas of distinction: area of articulation, manner of articulation, and voiced or unvoiced. The area of articulation refers to where the sound is formed, manner how it is formed, and voiced/un refers to whether or not the vocal chords are engaged during the sound's formation. Let's take an example /d/.
/d/ is called a voiced alveolar plosive. This means that the sound is formed by placing the tongue on the alveolar ridge of the mouth (the bump just behind your upper teeth). It is a plosive, which means the sound features a complete stop in the flow of air, as opposed to, say, a fricative (like /f/) which entails a partial impeding of the flow of air, and it is voiced.
/d/ is phonetically similar to /t/ because d is a voiced alveolar plosive, and /t/ is an unvoiced alveolar plosive. /d/ is also phonetically similar to /z/ because while /d/ is the voiced alveolar plosive, /z/ is the voiced alveolar fricative. In other words they're sounds which are identical except for a few small differences.
Presumably you are referring to words which are phonetically similar, which is how linguists determine a language's phonemes. This means finding two different words which are identical save for one sound. For example the English words /kæt/ and /bæt/ (cat and bat, pronounced in Standard American English). The two words are pronounced near identically with the exception of their first consonants: /k/ and /b/. Because other than these two sounds these two words are identical and yet have different meanings, we can identify that /k/ and /b/ are distinct phonemes in the English language. You can and Linguists do do this with thousands of words.
