An ELT Glossary : Reformulation (Discourse)

Reformulation is a discourse relationship in which a second idea is seen as a restatement, using different words, of an earlier one.  It may be used...

a)  if the speaker feels they have not made their ideas clear, so that the listener(s) may not have understood - for example : I'm researching into gastropods - that is, things like slugs, snails and winkles... 

b)  if the speaker wishes to modify what s/he has just said in some way. For example :  He was really happy about it - or at least, he looked happy.

Common markers of reformulation include : in other words, namely, that is, or rather, or at least, or better, i.e., To put it another way, What I mean is... etc