Working out tends to be divided into two groups: cardio and resistance. Cardio is what gets your heart beating faster and includes running and walking, and using the cycling and rowing machines in the gym - or of course actually doing those two activities. Actually any activity gets the heart beating faster, but of course it's easier to achieve results more quickly by doing it more intensively.
Resistance training is often thought of as being less necessary, but it does play a very important part in maintaining and increasing your health. It isn't only what is normally thought of as just lifting weights; it's called resistance because you are using your body to resist a weight - which can be something you lift or something you push against, which can include your own body.
One of the great things about resistance training is that it can be done at home with no, or a minimal amount, of equipment. A classic example are press ups, which uses just your own body weight and is, in my experience, one of the harder exercises to achieve.
It has many health benefits, particularly if you are getting on a bit. Apparently, the number of muscle fibres declines with age. From age 30 to age 70 we can lose more than 25% of the type 2 muscle fibres in our bodies (type 2 fibres are our strength fibres). Resistance exercise can slow down or even reverse the ageing process by building muscle mass and strength. Which, as someone who isn't a spring chicken, sounds pretty good to me.
Strength training covers a lot of bases, which includes improving bone and joint functions, bone density and muscle, tendon and ligament strength.