A book-entry account is an account meant for the management of electronic securities and storing various securities such as equity or bonds. It is kind of like an electronic folder for your shares: instead of physical paperwork, your ownerships are marked and displayed on your book-entry account.
It might not be necessary to store all your securities in this manner. Some unlisted companies have, however, changed their shares to be a part of the book-entry system, in which case they need to be stored on a book-entry account. Storing and trading listed shares also happens via book-entry accounts so in many cases it is a requirement for investments - and many active investors are likely to already have one.
When you open up a book-entry account, it is linked with a traditional bank account. The cashflow related to your securities is handled through the bank account: if you buy or sell securities that need to be stored on your book-entry account, the money will be paid from or paid to the linked bank account.
You can open a book-entry account for example in all of the regular banks and manage it using your online banking ID. Some other financial institutions and companies (e.g. Nordnet) also offer book-entry accounts. The easiest way is usually to contact your local bank and ask them about the terms they offer for an account like this. It can pay off to do some comparisons, however, because other players might offer better terms.
Banks can have limitations, for example whether or not you can have only domestic or also foreign securities on your book-entry account. There are also differences when it comes to storage fees and transaction fees when you buy or sell securities; whether you use the account for listed or also unlisted shares can have an effect as well. The fees are not usually very high, but it's always smart to look into them: a good place to start can be for example this comparison made by Taloustaito in spring 2019.
Opening a book-entry account is not very complicated - contact your bank for an offer and don’t be afraid to compare offers according to what type of investments you are planning to make.