Why are "they" asking you to sign? Keep in mind, if you meet someone briefly and they want to immediately sign you for anything, it's usually some hidden agenda at work, and usually not in your favor. They can take the quick approach: “do it now or they just might change their mind” and “you'll be a nobody for the rest of your career”. They also hope you don't read the contract, or at least not understand it or ask questions. Read carefully for your financial obligations and don’t be shy about seeking clarification if needed. Do they stand to make money only when you make money or will you be charged monthly fees?
In its pure essence, an agent or manager would want to sign an actor because they believe they can effectively manage, augment their talent stable, submit or otherwise significantly advance an actor's career - and both profit from the relationship, including financially.
Keep in mind that signing you may be a way of getting you off the market and their regulars a better chance. (This is where you could actually have something to fear. Generally, this practice is done in the major markets moreso than commercial markets.) You stay home, their favorites go out. Good questions to ask: how many of my types do you have? What kind of calls are you getting? What kind of clients do you work with? Legitimate, adult questions and answers you should know.
The adage, "if it sounds too good to be true, it usually is" really applies here.
NEVER sign a contract upon first meeting or even the second meeting. Read it over in the quiet and privacy of your home. Take that contract and have a theatrical attorney review it. Don't be afraid to ask legitimate questions. A workable contract will detail your relationship, what is expected from both parties and when. Who is responsible and obligated for what.
Is signing a good thing? If it is thought out and a fair contract for both parties, yes. It also means an agent will promote you more than their unsigned clients. You will have first crack at the jobs. You're on the A List. Doors should be open to you otherwise not open to you.
A management contract can get you the needed agents and opportunities that they can provide.
And even if you are signed, always keep in mind, you still must continue to advance your career on your personal level as well. That includes staying current in your audition skills, training, headshots, and current industry trends.