UHF Television antenna, might have a built in amp from the connection (does it have a power supply on the antenna feed??) No way of telling the bandwidth or gain without exact dimensions down to the millimetre and a lot of calculations
---------- Post added at 22:07 ---------- Previous post was at 21:04 ----------
Further to your PM the number of elements determined as such..
A yagi (this type of antenna) has three type of elements
Reflector (the rear most element is counted as a single one even though it might consist of more than one)
Radiator (the element attached to the feeder cable)
Directors (the elements in front of the radiator)
Your antenna (not a clear picture) looks like it's got 9 or 10 directors, 1 radiator and 1 reflector making it a 11 or 12 element Yagi in a horizontal polarization (though it could be mounted vertical). Quite acceptable for digital reception in a fringe to medium area though still hard to tell if it's wideband or single band so suitable for the fullo range of digital channels (digital channels use the full range of the UHF tv spectrum unlike analogue that used a small section of the uhf tv range)