The original Bittorrent client
The application itself is not illegal, nor is it illegal to have the application on your devices. The misconception that it might be illegal comes from the fact that it is often used to download pirated media, which is illegal. Simple having the app and using it is not inherently illegal.
The official application itself is perfectly safe, though dangerous media could be downloaded using it. It is also worth noting that there are modified versions of the application that are not safe. Always verify the source when downloading software. In this case, you should download only from uTorrent's official website.
The application is not a VPN, though the developers have made it very easy to use a VPN with the application. This can be done by going into the settings and entering the details of your VPN in the VPN section. Many sites strongly recommend using a VPN with torrent software.
uTorrent Remote is a mobile app which allows users to access the app on a computer elsewhere, such as at home, in order to manage their torrents. Torrents are particularly used for large files, so it can be helpful to be able to start and stop downloads from remote locations.
The purpose of the application is to provide a user friendly interface with which to manage multiple torrent downloads. Torrents are a peer to peer file sharing format that is particularly suited to sharing large amounts of data. Using this application, torrents files can be downloaded, paused, stopped, prioritised, and more.
Torrenting involves a number of different sources all simultaneously uploading and downloading data. When a client is "seeding", it is uploading information to other clients who are downloading it. The more seeders a torrent has, the more readily available the data is, and the faster the files can be downloaded.
Because the application is simultaneously downloading and uploading data it has already downloaded, it will need to verify the integrity of that data. This usually doesn't take long, though the amount of time is affected by the size of the torrent. Moving files that are still being seeded can cause errors.
To download the client, simply navigate to the official website, and click "Get uTorrent For Windows". If you are not using a Windows platform, click on "Other Platforms". You will then be presented with options such as Free, Beta, etc. Once downloaded, run the installation software and follow the instructions.
Sometimes it is necessary to stop seeding a torrent file. This can be the case if data usage restrictions apply, or if you need to delete the seeded data from your system. To do so, simply right click (Command Click on Mac) the desired torrent listing, and select "remove torrent".
Though there are other reasons why downloads may be slow, the most common reason is a lack of seeding peers from which you can download the desired data from. The more seeds a particular torrent has available, the faster that data can be downloaded. Fewer seeds means a slower download time.