Building things, real things, physical things, is hard. If you want to do a digital painting, and you have a computer, you can get all the necessary software and supplies for a relatively low outlay of cash to paint whatever you might want to paint digitally. Writing is essentially a free endeavor, though buying some equipment will make it easier. Recording music, nowadays, can be done for little more than the cost of an iPad. But if you want to build a table or a robot or a house, you're going to have to pay for a lot more than a tablet or computer.
This is one of the great strengths of a Makerspace. Think of it is a gym for making stuff. The idea is that you pay a membership fee, and that fee entitles you to use any of the equipment that they have available. Equipment that you, as an individual, would have to pay a lot of money for if you wanted to buy it on your own. Even better, you don't have to buy an enormous new house to store all of the new equipment; it's all stored for you.
Of course, just having access to the equipment does not a Maker make. There are generally two more advantages of a Makerspace. The first is that they'll offer classes on using the equipment, and for some equipment, these classes will be mandatory. There is often a positive correlation with how useful a piece of equipment is and how likely it will be to cause you serious harm if you don't use it properly, so let's learn how to use stuff. Even if you don't harm yourself, you could harm the equipment. Training is a good thing.
The second and greatest advantage is the community of patrons that you will find at the Makerspace. Cool equipment and space tend to draw cool people along with, and these people are often quite happy to help show someone how to better attach two pieces of wood or how to properly connect a solenoid or do just about anything. They won't finish your project for you (and where would the fun be in that), but they can give you helpful tips from years of experience on how to best do the thing you're doing.
Like a gym, these spaces tend to work on contracts, and for the same reason: to keep costs down, they need a certain percentage of their paying customers to not show up all of the time. If you could just pay for the times you show up, then the costs would be significantly higher for each visit. One of the bigger chains of Makerspaces, TechShop, has monthly or yearly memberships, depending on the location.
The gym model isn't the only way to go. With financial support, non-profit, community-oriented Makerspaces are another way to go. You can check out the Mt. Elliott Makerspace, and see more in the video below.
There are Makerspaces in many areas, though sadly not everywhere. Make Magazine maintains a list of spaces and community groups on their site, so see if there's one in your area. Make Magazine even has workshops on starting your own Makerspace. Though that event has passed, hopefully there will be more in the future.