Cybersecurity protects from attacks via cyberspace (that nebulous entity we have all created to work and play in via our technological devices and linkages). This form of security covers your computers, smart phones, laptops, and other hardware as well as the means of accessing, linking, and communicating through them (think LANs, the internet).
Cybersecurity attacks may target a website your company keeps but are more likely to target the data your company stores and uses to run your business. This is why information security is important to understand.
Information security concerns itself with the actual raw data your company collects (such as a field requiring a date: MM/DD/YYYY) and the information derived from that data (e.g., a DOB versus a policy renewal date). This information may be stored digitally (say on a server via the cloud), in an analog format (think about forms or photos in a file cabinet), or both (perhaps a thumbnail drive within a desk drawer).