Нам есть, чему поучиться.
I assume the entire phrase means something along the lines of "we could learn a thing or two from them/that", but I'm not sure how to parse this construction, interpreting it more literally.
I guess it can be parsed as follows
There's (that) which is for us to learn
In Russian it's an impersonal construction.
The reverse construction would be
У нас есть чему поучиться - We have (that) which is to be learned
что is inflected in Dative as чему because this is the case in which the verb учиться accepts object denoting the item of learning.
object in Dative + есть + relative pronoun + infinitive is a stable construction.
Нам есть куда пойти - We have places to go (there's no shortage) more lit. There're places for us to go
negative Нам некуда... - We have no...
Им есть что смотреть - They have something/things to watch (there's no shortage)
negative Им нечего ... - They have nothing ...
Мне есть зачем жить - I have reasons to live/what to live for
negative Мне незачем ... - I have no reasons to live/nothing to live for
Нам есть чему поучиться.
It's an impersonal sentence which is formed with the verb "to be"(есть ), an object in the form of a pronoun in the dative case(чему), another verb in the infinitive form (поучиться)functioning as an attribute to the object, and the agent of the action expressed by the infinitive also in the dative, which is traditional in impersonal sentences. It corresponds to English
There's something to learn for us.
There are a lot of sentences of this kind and there's never a comma in them.
The phrase is typically about learning from somebody's unique or superior skills or knowledge, not about getting any missing knowledge (that somebody is often known from context and can be omitted):
Нам есть чему (у него, у них) поучиться.
So I'll try to literally parse it this way:
There is something for us (what) to learn (from them) for some time.
Word by word, parsing it backwards:
There is (something) - есть (то)
for us - Нам
(what) to learn - чему учиться
to learn for some time - поучиться
Поучиться as opposed to учиться means that there's a limited opportunity ('while possible') to learn from somebody who's definitely not hired for teaching.