Concentration's Meaning

I've read a few answers and concluded that for most of these answers, concentration in meditation often implies unawareness of peripheral stimuli. This confuses me. I usually have wisps as thoughts rather than full blown thinking in meditation, but I don't particularly become unaware of my environment. **Is such an experience very advanced? More so, does unawareness imply literally not seeing/hearing/etc. or merely not being solicited by such distractions?** Finally, I'm wondering whether the diminution of thoughts *in itself* means little. **Is attention placed upon the object consistently more important than thought reduction?** For example, I can imagine attention being close to the object but thoughts (e.g. about the object) arising, but I can also imagine a thoughtless person's attention being fragmented, directed without focus. **Is any of these more important?** Thank you