CASify
What symbolic means
An ordinary calculator only knows numbers. Whatever you give it, it works out right away and hands you back a decimal. It can't do anything else, because inside it stores nothing but numbers.
A CAS like the TI-Nspire CX II CAS works one level above that. In Europe it's called the TI-Nspire CX II-T CAS and works exactly the same way. It treats an expression as a mathematical object it can handle without working it out. To a CAS, a letter isn't a stand-in for a number it doesn't know yet. It's something it's allowed to calculate with. That's why it can rearrange, cancel, solve and differentiate without knowing what x will turn out to be. That's exactly what the word symbolic means.
This leads to the second difference: results stay exact. An ordinary calculator rounds straight away and keeps working with an approximation from then on. A CAS keeps the exact value until you say at the end that you want a decimal now. In problems with several steps, rounding errors add up in the first case. In the second, there aren't any.
Two examples make this concrete. On an ordinary calculator, the square root of 2 comes out as 1.414213562. On a CAS it stays √2. And if you ask a CAS to solve x² minus 5x plus 6 equals zero, it answers x equals 2 or x equals 3. A calculator without CAS can only draw the graph, and you have to read the points off it yourself.
What you can do with it
Simplify and factor expressions. Solve equations and systems of equations, even ones with parameters in them. Differentiate and integrate, in general form too. Work with matrices and vectors. Find limits.
In upper secondary school, you'll notice this most in calculus. To find a maximum or minimum, you differentiate, set it to zero and solve. With a CAS that's three inputs and an exact result. Without CAS you draw the graph and read off an approximate value.
A CAS doesn't do the problem for you. It calculates the part you write down for it correctly. The approach, meaning the decision about what to calculate in the first place, is still up to you. That's why schools can allow these calculators in tests.
Why some schools are switching
In some places a CAS is now required, or soon will be, and the graphing calculator without CAS is being phased out. Whether that applies to you depends on where you go to school. Your school or exam board decides which type of calculator is allowed, and your school decides which model to buy. So don't buy anything until you know. Some exams don't allow CAS calculators at all, others require one. Check with your school before you buy.