As has been described, it will follow a phugoidal path which will result overall in a net loss of altitude. This is all due to a basics law of phsyics, namely Netwon's law that states (and I paraphrase for the sake of clarity) "A body will remain at rest or at a constant speed unless a force acting upon it causes it to change".
When an aircraft is in level flight at a constant speed then all the forces acting on the aircraft are equal and opposite: the downward force acting on the aircraft (its weight) is counteracted by the equal yet opposite force of lift which is generated by the aircraft's wings. It is crucial to note that the amount of lift the aircraft's wings generates is proportional to the speed the wing moves through the air (airspeed). This speed through the air is maintained by the engines producing an equal and opposite force to the drag caused on the aircraft by the air which tries to slow the aircraft down.
Now assuming the aircraft is trimmed and stable and maintaining a constant speed and altitude when you remove the power, the aircraft will begin to slow. This is because the force of drag is now greater than the forward force of the aircraft (which is now purely momentum as the forward force of the thrust has been removed). This reduction in airspeed causes a reduction in lift. The reduction in lift causes the aircraft to begin descending as the downwards force (weight) is now greater than the upwards force (lift). However, as the aircraft descends the aircraft is accelerated due to the force of gravity. This acceleration causes the speed to increase. As the speed increases, lift once again increases until it is greater than the downwards force of the weight, at which point the aircraft will start to level off and gradually climb. As the aircraft climbs, the drag caused by the air along with gravity (now slowing the aircraft) will cause the speed to reduce until once again the resulting lift is reduced to the point it is less than the weight, adn the aircraft begins to gradually level off and descend again. Rinse and repeat
As a result of this, although the aircraft does regain some altitude when it climbs again it will never reach the same height as it started due to energy being lost to friction with the air, and thus the aircraft will actually be effectively descending gradually until it hits the ground. This is similar to dropping a bouncy ball on the floor - you will notice that unless you throw it, it will never return to the height it was released from as energy is lost as the ball deforms at the bottom of the bounce.
NB: It is also important to note that the aircraft will not enter a phugoidal state if it doesn't reach or exceed the speed it was trimmed to fly level at before power was removed. This could be the case if for some reason the aircraft was operating at a high power setting and thus higher speed than normal. In such a case accelerating force due to gravity in the descent would be overcome by the drag caused by the air before it reaches the trimmed speed. In this case, the aircraft may enter a gradually steeper descent which will then reduce as the aircraft's speed increases, but it will never actually level off or climb.
NB2: This is a very simplified model and does not account for thermals and winds which occur in the real wolrd and would/could significantly alter the path of the aircraft depending on their strength.
NB3: Your experience may differ depending on the specific aircraft but roughly speaking from analysis of the forces involved this is how the aircraft would react. Terms and conditions apply. No refunds. See website for details.
Hopefully this image (courtesy of NASA) will clarify things a bit more.
Imagine the aircraft is in flight, and imagine the size of the arrow shows the size of the force. The Lift and Weight arrows act in opposite directions but are the same size so they counteract each other meaning overall the aircraft neither climbs nor falls. Same goes for Thrust and Drag: it is neither speeding up nor slowing down. It is in level flight at a constant speed. Now remove thrust. Drag is now greater than thrust, reducing airspeed. Lower airspeed means less lift. As a result Weight is now greater than Lift. Aircraft falls. etc.
Hope this helps.