Question

1. to avoid doing or having something
2. avoid doing or having something
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It is the definition of 'skip.'
Why is 'to' put before 'avoid'?
Can't we use #2 as the definition of 'skip'?

Answer 1

First of all, I'd need to see 1 and 2 in complete sentences. Context will determine whether "to" can be omitted or not.

And yes, these expressions can mean "skip."
http://www.merriam-webster.com/dictionary/skip

Answer 2

The basis or root of English verbs is the infinitive which is the verb preceded by "to." Most dictionaries use "to" in the definitions of verbs.

Informally, it's fine to omit "to" in a definition.