What is strength? Strength is a measurement of how much weight you can lift or move. To really improve your strength, weights can be useful, but is generally not needed. Here's a personal anecdote - I managed to successfully increase 40kg on my bench press from doing 500 pushups a day!
It is quite common for people to go to the gym or attend fitness classes to improve their strength, as these often include fitness equipment which does help with increasing strength.