What makes speaker's sound big?

This is a not so well defined criteria. Some call the soundstage size an expression of BIG sound and some consider bass extension the criteria for BIG sound.
 A truly big soundstage comes from speakers with very low distortion artifacts and minimal diffraction effects. Diffraction and distortion effects are non consonant and detract from the soundstage scale. Low distortion bass extension is well understood.

Hello Martin, I just read your post and haven’t gone through the responses. Excuse me if I may repeat something already mentioned. I’ve been in this hobby for 25-30yrs. So one of the things I offer is experience. The design of the speaker is what makes it sound big. Components and cables can significantly affect the size of the sound but the largest factor is the speaker. For the most part, larger drivers do produce larger sound but there are exceptions to this rule. At times, a well designed small driver in a well designed speaker can sound very big along with a larger driver in a poor designed speaker can sound small.  My advice, if you really, really like your speakers, try higher level cabling to hear if the speakers open up. If not, try upgrading your components to items that are much more “open” sounding. If these basic attempts don’t work, then I don’t think the speakers you have are really meant to be open, big sounding.  

Hello Martin. I've always had big speakers as my listening room is rather large. I've just changed to smaller ProAc speakers on sturdy heavy stands and added two 15" sub-woofers. One on each sides. The sound is pretty big and it will fill the room quite easily. I think the only draw backs will be the SPL your small speakers will deliver. If your trying to have a rather large and loud party, this set up will probably not do as usually, the power is limited with smaller woofers. The good part is that the small footprint your bookshelf speakers will have, is going to give you a better musical stage definition. 
The previous speakers where OBs. The thing I miss the most is how quickly they reacted to the music. But I do not miss the added space they took in my listening room (living room). I will have to put them up for sale as I rather like the added space that I get with the small speakers. You can't win them all.

Big Speaker:)

the answer is yes, you need a big speaker for big sound, while you can produce a reasonable sound stage out of a smaller speaker there will be no impact or force from a mini speaker. Mini or small speakers will always sound mini or small, its just physics and anything else is just a illusion or delusion or whatever you want to call it.
A big planar speaker with a big surface area will sound bigger, an array of dynamic speakers emulating a planar speaker will sound bigger. If you combine a big sub woofer with tiny speakers you will get impact from the subwoofer but the rest of the musical spectrum will still sound small - like the small speaker where the sound comes from. Same like the other poster said: a big block engine will always sound bigger than a tiny 4 cylinder engine, even blown up to deliver hundreds of horses, if you want big than go big - and yes again bigger is better as long you have room!