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Transcribing solos means, you listen to the music and write it down, bit by bit. Someone's solo = their improvisation. If it's simple/slow enough that it's quicker to learn it by playing along, just do that. (I've never needed to transcribe Louis Armstrong, but have just learnt by playing along with him.) If it's very fast (e.g. Bird, Coltrane) you might need to slow it down to transcribe it. You learn how to transcribe it by doing it, it also trains your ear in recognizing melodies, harmonies, chord voicings, rhythms, forms.

You can buy books of solo transcriptions, but I've found that they're absolutely useless. (and always inaccurate) Maybe it's like reading a book vs. typing it out?! hehe. At first glance I couldn't see how typing a book out would help anything, I mean, it's already written down for you! The main element of learning by working out bit by bit what it is, isn't there. But there are elements in common - it's a little like playing a solo you've written down, and you would absorb the word patterns if you typed a whole novel I guess.

Ear training gives you this skill

e.g. https://www.youtube.com/watch?v=KhyyjRcrn84

Transcription is the latter -- create a paper version from a recording. Same as medical transcription is typing up dictated notes.