Split infinitives are a specific type of misplaced modifier and should be avoided in formal writing.

An infinitive is a verb preceded by the word to: (to write, to examine, to take, to cooperate). When an adverb appears between to and the verb itself, we get a split infinitive.

• INCORRECT: She wanted to immediately accept the job offer.
• CORRECT: She wanted to accept the job offer immediately.

Really, completely, entirely, and unduly are often used as split infinitives in spoken English.  In formal writing, it is considered bad style.

• NON-STANDARD:  It's hard to completely understand why he would make this decision.  
• CORRECT: It's hard to understand why he would make this decision completely.  

Sometimes avoiding the use of a split infinitive creates ambiguity.

• NON-STANDARD:  Jason was told to occasionally visit his advisor.  
• AMBIGIOUS: Jason was told to visit his advisor occasionally.  

The above sentence creates ambiguity.  Is occasionally modifying told or visit?  To resolve this, move occasionally right after the verb it modifies. 

• CORRECT: Jason was told to visit occasionally his advisor.