You’ll have to talk to HR and/or representatives from the company they use for their benefits for specific details, but in general:
A defined benefit pension means that when you retire, the amount of money you will get is already defined (it’s not clear how much that will be in this case- it sounds like this one will give annually a little over half of the highest salary earned during the career, if he works for 32 years- and presumably less depending on how long he works there). In this case it sounds like the pension is fully funded by the employer, so it’s an additional benefit that your SO won’t have to pay for, but that they are investing on his behalf.
Defined benefit plans are great and VERY rare these days- this style of pension is very costly to employers but it gives you a lot of security knowing that you will for sure receive $X upon retirement. Historically, this is the kind of plan most people think of when they think “pension”- the guaranteed annual income that, say, retired military or government workers get. As you might imagine, this kind of retirement plan encouraged a lot of people to stay at one company for their entire career- but it could also be devastating financially when people lost their jobs near the end of a long career and with it, the pension they’d been counting on.
A 401K is a tax-deferred way of saving money for retirement- you should DEFINITELY contribute at least the amount the employer will match, as that’s free money. $300 a year is low for an employer match, but not surprising if they also have a defined benefit pension in place. They’re already contributing way more to that than even the most generous match plans. You should contribute as much as you can comfortably to this, as it’s pre-tax, so you’re lowering your taxable income and with it saving tax dollars. It is expensive to take money out of a 401K before retirement, though (you have to pay fees when you take it out early, and taxes no matter what) although some plans do allow you to withdraw money for specific uses with few or no penalties, so look in to that.
A flexplan is a savings account for health or childcare expenses that you can contribute money to before taxes, which also lowers your taxable income. You select the amount you want to put in it that year at the same time as other benefits (so during open enrollment or when you’re hired or have a status change. You usually have to use it before the end of the year, though, or lose it, and you must keep immaculate records as they can ask to see that you spent it only on qualifying expenses, and if you can’t prove that, you can lose the remainder of the account. It’s a great idea, though, especially if you know you have a big or regular medical expense coming up (wisdom teeth, allergy testing, whatever), to put in enough to cover copayments, deductibles, or prescriptions. You don’t NEED it but it’s a nice benefit.