I can't speak for South Africa specifically, and I'm by no means an expert, but since there are no other answers, I'll chip in...
Saving is generally a good thing to do, so you should find a home for any 'spare' money at the end of month. Even if it's just a few quid/bucks/rand, it's still better to save it than to start thinking you're rich and squander it on something ;-)
If you have any non-mortgage debt - pay that off first before considering any savings. Pay off credit cards first, then bank loans. Essentially, check the interest rate and pay off the highest ones first.
After that, not all savings are equal. Depending on your local rules, a pension is (probably) tax free while it's in the pension. That is, you pay in (perhaps with your pre-tax salary), the money stays inside the pension and you only pay tax when you get to retirement age and start withdrawing from it. In that sense, it's quite a good deal - because you get to grow the whole of that money, without losing a load of it to tax first.
Pensions usually have lots of rules though. You won't be able to take anything out of it until the maturity date (usually your retirement age - whatever you specify when you set it up). Even then, you may only be able to take a monthly payment, or maybe you'll be allowed to take a lump sum up to a certain percentage of the total. What taxes you pay on that "withdrawal" are also rules you should look into.
All that said, pensions have provided a service for generations, and so may be a suitable place for some or all of your savings. You should speak to a professional to work out the best way to proceed though - as things get far too complex very quickly.
There is of course also a regular bank savings account. These tend to pay small interest rates, and tend to be taxed (that is, your interest payments will be taxed if they're big, or if you earn lots of money elsewhere). As such, they tend to be a poor performer for long-term savings, although are useful for short-term savings (especially while saving up for something). You also can't put pre-tax salary into a savings account, so the amount you actually get to earn interest is less than it would be in (say) a pension.
In the UK there's also something called an ISA, other countries have differently named products that may or may not be on the same lines. It's essentially a bank account, but once money is inside it, it's immune from tax. That means you get credit interest and the taxman can't take any away. Thus, each month you earn a greater rate of interest. There's a variant of the ISA which allows you to invest in stocks and shares - any gain you make on that investment is similarly tax free. You get to be your own banker here, and of course if you invest poorly you could lose your money.
The main advantage of ISAs is that you can withdraw the money any time you like. There may be some tax to pay if you happen to have made lots of money while it was in the ISA, but it remains a flexible way to save money. If you're prone to seeing a big bank balance and withdrawing the lot to 'waste' it, then an ISA may not be for you though ;-) Also, there's no way to pay into an ISA using pre-tax salary, so accumulating money in an ISA is slower than into a pension.
If you have a mortgage, then you could also consider over-paying on that each month. It means you'll pay it off sooner, or will be able to 'trade up' to a bigger property or whatever sooner. By reducing the balance, you're reducing the interest on it, which reduces the monthly cost to you - a virtuous cycle, although it doesn't leave you with any ready cash to spend if you need it.
Lastly, you could directly invest your money. To buy anything you probably need a fair bit of money, and so you'll need to save it up first. A regular bank account or ISA-type account may be a good way to do this. However, once you've got your stake and invest in something (eg. real estate), then your money is tied up and will take a while to 'liquidate' back into cash if you ever need it. The benefit is that you get to control the investment and if you play it well could make more money than any of the savings options.
In short - I'd definitely advise some sort of saving. It's probably best to save a bit into different solutions, rather than just one. Some sort of 'retirement planning' sounds very boring at the age of 23, but it's worth having some sort of a plan because you'll get the advantage of more years of growth on your savings than if you start it at (say) 43.