Tienjarige tafels (ten-yearly tables) are contemporary indexes on the civil register. These tables used to be the only way to access the BMD records of the civil register, but with the large number of modern (usually online) indexes created in the last few years, they have become less important.
Why were they made?
Because it's hard to find a record in the civil register if you don't have an index. At the end of each year, the registrar created an index for that year, usually at the back of the folio with the records. But if the year for an event was not known, it could still be difficult to find the record someone was looking for. Therefore every ten years an index over the previous ten years was created, usually in a separate folio. The first one was created in 1823, covering the years 1813-1822.
Nearly every municipality created tienjarige tafels for its BMD records, but there are exceptions. In The Hague, for example, there is a single table for marriages from 1811-1852 (but births, deaths, and marriages after 1853 are indexed in tienjarige tafels).
What information do they have?
Indexes on birth records usually contain the name of the child and the date the record was created, and often the sequence number of the record. Note that the date in the index is not necessarily the date of birth! The child is indexed under the surname he had at the time of birth. If he was born before the marriage of his parents, that will be the mother's name, even if he received his father's name at the marriage! Therefore, if you can't find a birth in the index, search also for the mother's surname.
Indexes on marriage records will have the names of both spouses, the date the record was created, and often the sequence number of the record. The date listed is usually (but not always) the date of the marriage, as nearly all marriage records were created during the marriage. Usually you can search the index on the name of either spouse, but in some places (e.g. The Hague) the tables are only indexed on the man's name.
The indexes on death records have the name of the deceased, the date the record was created, and often the sequence number of the record. Note that the date in the index is not necessarily the date of death!
The tables are sometimes sorted alphabetically, but more often sorted on the first letter, and per letter sorted on date. On the image above (click to enlarge) the table is sorted on surname, and per surname on date.
Note that the tienjarige tafels are merely an index. Use them to find a record, and never as a source by themselves!
Where can I find them?
At the same place as the BMD records of the civil register. Like the BMD records, the tienjarige tafels were created in duplicate, one copy for the town hall and one copy for the district court. You will find the tables with the registers in the provincial archives, and in local or regional archives. There are microfilmed copies of many tables in the study room of the Central Bureau for Genealogy in The Hague and in the collection of the LDS (usually available for consultation in family history centers worldwide).