That bike will be fine on relatively smooth trails.

It would be fine on smooth but muddy / loose dirt / loose gravel trails too but you might have to put knobbier tires on (I can't really tell from the picture what it has)

Look at the chain ring and make sure it's not badly damaged or worn out. (Though from the pictures it doesn't look like it is)

Make sure the chain doesn't have any jammed linked where it doesn't bend. Just cycle the pedals backwards and look at the rear derailleur. You'll see a jammed link real fast as the rear bends the chain both directions.

Make sure both shifters work. If they physically move the derailleurs but it still doesn't shift super smoothly or doesn't stay in gear, I probably wouldn't worry about it. It may just need a quick tune up. If it was never tuned up after it was originally purchased it will probably need one. You can either learn to do it yourself (easy to do with 9000000000 Youtube videos on it) or pay like $20 at any bike shop.

Make sure the brakes work. They are hydraulic brakes. You should not need more than 1 finger gently pressing the levers to completely lock each wheel, meaning that while you're on the bike with your weight pushing it forward, you should be able to completely stop it from moving with each wheel independently. Conversely you should not hear drag or rubbing of the brake rotor when its' spinning through the brake caliper. If you hear 1 rub each rotation it means the rotor is warped and is very fixable. If you hear a constant rubbing it means the pads aren't letting up enough and is PROBABLY very fixable but COULD be a bad caliper that isn't self adjusting properly.

Spin each wheel and watch it. Make sure it doesn't wobble. If it wobbled back and forth it's out of true. It's easily fixable but you need to know about the issue.

The fork has a lock out knob on the right side. Make sure it works. When engaged the fork shouldn't work. It should be totally rigid. When disengaged the form should bounce up and down when you lean weight on it. (When riding on the smooth trails keep the fork locked. It'll sap your power with no obvious gains. But I do feel it has a use. I have the same fork on mine and it's great for those times when I need to take cut through over curbs and down root filled trails. Do not mistake it for a true mountain bike fork that can be heavily abused.)

When test riding it make sure nothing makes any clanking or grinding noises. A gentle click click click click is normal when coasting (not peddling) but it shouldn't be making any loud metal on metal sounds. The wheels should spin freely for a long time if you lift the bike up and spin them. It they slow down and stop in 10-15 seconds something is wrong. A decent wheel should spin for like a minute.

Look for any obvious signs of a cracked frame or that it has been kept outside in the rain. For the cracks look at the weld joints. If any of them look to be cracked walk away. For it being kept outside look at the bolts and screws. Especially any unpainted ones you can find. Look for the bolts holing the brakes on, the ones under the seat holding it on. Stuff like that. If they are rusted the bike may have been stored outside in the rain and may have moisture inside the frame that could cause problems. The screws on the front derailleur are often a dead giveaway and I can see they are shiny and new.

In the photos the chain and drive train look clean. Like REALLY clean. They may have a dry lubrication on them which is good. They may not have any lubrication on them which is bad. Make sure the chain and cassette and chain rings don't look beat to hell. They should be scratched up a little bit because there is metal rubbing on metal. But there should not be gouges out of the chain or gear teeth. Google 'worn out chain ring' and look at photos like these....see how the paint is worn off? That's okay. See how the teeth are much shorter and pointier on the right? That's not okay. An unlubricated drive train will make that happy much faster than it normally would.