Say for a moment you have a file server with three 1Gbps NICs that is easily capable of saturating a 3Gbps link with any file, and a computer that also has three 1Gbps NICs and is capable of receiving and processing 3Gbps worth of traffic. You set up the three 1Gbps links on each end into a single 3Gbps trunk directly between the file server and your computer, and then try to transfer a file.
My understanding is you will be limited to 1Gbps for this file transfer, because even though the link can do 3Gpbs, it's still three separate 1Gbps links bonded. But now say you try to download 3 files. You'll find that you can get each file at 1Gbps, for 3Gbps total throughput.
Of course, this is a contrived scenario. What's much more common is you have network switches in multiple locations. These switches support many users that all have 1Gbps network ports in their computers, and a few servers that may have multiple nics, or even 10Gbps or higher network connections. What you may find is that 1Gbps is not enough throughput between switches. Individual users can't take more than the 1Gbps link between switches, but in aggregate a number of users can easily saturate that link. And it might be very costly to get faster single links between switches.
So what do you do? It turns out it's very common that the link between these switches is fiber, rather than copper (though copper can work here, too), and that multiple pairs of fiber (in a single cable) were pulled between the switch closets for redundancy; some of those pairs are currently sitting dark. So you get a few extra SFPs, pop them in some free ports on each switch, set up an LACP trunk, and in this way get higher throughput between the switches.
Now it doesn't matter that individual sessions (and endpoints) are still limited to 1Gbps, because you don't really need one person to use more than 1Gbps. This is about supporting a whole set of users at the higher speeds.
Additionally, you need to be careful how you set up the link. If you do things wrong (ie, you've never turned on spanning tree), it's easy to create a routing loop when you plug in the new link, and that can give you a real bad day in a hurry.
A final note here is that LACP links are resilient to one member of the link going down, so you can also use this a way to help protect against outages. Typically, the wiring is using the same cable path, and an event that breaches one set of wires will breach the other as well. But sometimes you get lucky.
You can also connect to different switches, to have redundant cable paths. This costs more (you need cable pulls between each of the switches), and in this case it's even more important to be sure you understand spanning tree, as well as the specific spanning tree types supported by your switches. Not every type of spanning tree allows you take much advantage of the redundant links in terms of increased performance, especially in older or cheaper equipment, and will instead simply disable the link until an outage in a different link changes the tree topology. But the right setup here on the right equipment can use these links not only for redundancy but also for increased throughput.