TypeLink pages are stored on a Mac OS server protected behind a software firewall. All requests from the webapp and the iOS app are checked for security, to make sure you have access to the page you're requesting (whether because it's your page, or shared to you, or shared publicly). The app uses industry-standard software libraries to protect against common security attacks (cross-site scripting and SQL injection).
We do not currently have an SSL certificate, so data is not encrypted in transit. Also, page data is not encrypted as it's stored on the server.
In general, TypeLink is reasonably secure for information you'd like to keep private, but it is not recommended for use to store things like SSN, passwords to other web sites, or business trade secrets.