I actually forgot to ask your location. I was mentioning headphones for a $200 Canadian budget. Only now realizing you mentioned the HD6xx, which are obviously more than $200 CAD.
You'd have a few more closed back options in the $200 USD price range, but I still stand by my 770 pro (80ohm version) recommendation.
It's difficult to really explain soundstage to someone new without comparing headphones in person, although @Kalm_Traveler1 describes it well. It gets complex, as it is subjective and lacks quantifiable graphs to actually show its performance.
Let's say you're playing Battlefield V, which has really good sound design, a headphone with a smaller soundstage will sound close to your ears, without much separation in distance of sound; It creates a claustrophobic sound. Headphones with wider soundstages have better separation and will sound "larger", better simulating an experience of being your character's shoes. It will basically sound less like you're wearing headphones, with all of the sounds coming from those two drivers right next to your ears. Headphones, in general, have a limitation on how well they can produce soundstage compared to speakers, but most Open-backs will outshine closed-backs, such as your Razer's.
Sound Signature is just how people describe the headphone's flavor of sound. For example, your Razer headset is most likely possesses a bass-heavy sound signature, which tends to bleed into mids and make it sound muddy or "underwater/congested".
Bass/Lows - These are basically your lower frequency sounds, think of sub-bass which is what makes your ears rumble or the lower frequencies of a kick drum.
Mids - A lot of instruments and sounds fit within this large range. Both Male and female vocals, guitar, piano etc etc.
Treble/Highs - These are high frequency sounds like a high hat on a drum, or the "SSSS" sounds from speaking
In the case that you'd consider open back headphones, there are a lot of options in the $200 price range.
- Sennheiser HD6XX aka HD650 (These are just a rebranded pair of HD650's, which are fantastic. I own a pair of HD650's, they excel with mid-range, which makes vocals really shine for when I'm listening to ballads for example. Treble is competent, avoids being sharp or piercing, and the Bass has a nice texture and sounds quite controlled. It's a relatively warm leaning sound. Soundstage isn't super wide, but it's definitely sufficient and natural. These are also very very comfortable headphones, more so than the DT770's i've talked about before. Since they're open-back, the design doesn't cater to isolation, allowing for the choice of earpad material to be much more breathable. Be aware, they can be a bit harder to drive/power than some others headphones, ie. you may need an amp depending on your motherboard.
- AKG K7XX aka K702 (I don't have too much experience with these headphones, but many people love these headphones. I've read that they have a very wide soundstage, wider than the HD650's, and it has a bit of a vshaped sound signature, with some recessed mids that sound a bit distant.
- HiFiMan HE-4XX or HE400i (I own the HE400i's, which I believe shares the same characteristics as the HE-4XX. I've heard that the 4XX's are a pair of 400i's with better comfort and build quality. These are planar-magnetic headphones, which is just a different technology used to produce sound. This allows them to have very nice and extended bass. These also have a wider soundstage than the HD6XX's. Mid-range is good, but there is less detail and aren't as forward as the 6XX's.
There are other great options as well, but massdrop has really lowered the price points on these previously mid-range $400 headphones making them a great value.
Hope I didn't just confuse you more!