Difference between 學習 and 學
Many Chinese words have both a 1-character and 2-character form

For example:


  eat = 吃 = 吃饭
  
  study = 学 ＝ 学习
  
  lion = 狮 ＝ 狮子
  
  coal = 煤 = 煤炭


Their usage is constrained by grammar and prosody

For example:


  Ungrammatical: 我喜欢吃
  
  Grammatical: 我喜欢吃饭
  
  Bad prosody ("sounds weird"): 我在学
  
  Good prosody: 我在学习


Sometimes the 2-character form is an expansion of the 1-character word


Dummy object for a verb (allows a transitive verb to be used intransitively):


吃(饭) &lt;-- Grammatically 饭 is the object, but as a whole it means "eat", not "eat rice". The object is a "dummy" object.
跑(步)
说(话)

Two characters meaning something similar (you can pick the form that works best for prosodic reasons):


学(习)
煤(炭)

One of the characters is a "dummy" word that means almost nothing (for making nouns into 2-character words for prosodic reasons mostly):


本(子), 狮(子), 棒(子), ... almost anything ending in 子
(老)虎
盖(儿) ...almost anything ending with 儿
木(头)



Sometimes the 1-character form is a shortening of the 2-character word


The word was originally a mono-morpheme polysyllabic word:

蝴蝶 (you'll sometimes see "蝶" used to stand in for "butterfly" in compounds)



Prosodic considerations in Chinese

I've alluded briefly to "prosodic considerations" in Chinese. But how are you supposed to know when to use the 2-character vs the 1-character version of a word?


Sometimes grammar chooses for you:


我要吃饭 (intransitive) vs 我要吃冰淇淋 (transitive)

When you're making compound nouns, it's usually the one-character form from each word (or even further reduction)


北京大学 -> 北大
高速铁路 -> 高铁



The following assertions are supported empirically, but they are not absolute


[N N] is almost never 1+2:


1+1 鸡蛋
2+1 商业区
2+2 人民广场

[V O] is almost never 2+1


1+1 请客 
1+2 丢面子
2+2 学习经济

There are exceptions to every rule!


我喜欢你 (喜欢 is basically always 2-characters, regardless of the object)



To address your question, let's look at 学习. 学 means learn; 习 means practice. As noted above, this is a case of expansion where both characters mean something similar. 学 and 学习 are identical in meaning, but one may be chosen over the other for prosodic reasons.

（论语）: 学而时习之，不亦说乎？ Isn't it a pleasure to study and practice what you have learned?