Japanese doesn't have pronouns the way English has pronouns. English pronouns are bare placeholders in a sentence. Japanese is much more strict about these things. It considers gender, social position, and in-group and out-group relationship. For that reason there are no actual pronouns in Japanese. Instead there are words that are used to refer to person without using their name, or when not referring to a person causes ambiguity in the sentence.
Boku is used in Japanese where in English we would use I. However, boku carries with it a couple of declarations.
1) The speaker is male.
2) The speaker is offering deference to the person he's addressing - either he is younger, less experienced, a subordinate, a social inferior, or is being deferential to a customer or a visitor from another company. (It gets complicated.)
In English we might say "this unworthy one," referring to ourselves, e.g. "Allow this unworthy one to conduct you to the president's office."
So what is tachi doing there? Japanese doesn't really have a plural, either. In English we have plurals for all countable nouns: Man - men, dog - dogs, child - children.
In Japanese that just doesn't happen. For a few select words (mostly ones that refer to people) it is possible to add a word to indicate there is more than one. There are several group words, and tachi is one of them. It is a grammatical suffix, not a word on its own.
"We ..." in a sentence in English means a couple of things, and we pick out from context which it is. It can mean we (including the speaker), or we (our team or family or business, but not including the speaker). Similar to how "we" in English leaves it to context to decide who all is included, Japanese also leaves us guessing, unless there's context. Boku tachi can refer to the speaker and his associates, or his family, or his company.
Wa (normally romanized as ha because that's the Japanese character used to write it) is a particle, one of a bunch of small grammatical suffixes that perform a variety of function. Wa is the topic marker of a sentence - a way to translate it in English is "as for -" e.g.
neko wa - as for the cat
otoko no ko wa - as for the boy
kuruma wa - as for the car
So we finally get to boku tachi wa. It is usually best translated as "as for me and my group," and then you can search for the best English words to make that sound less stilted.