Berachos, Chapter 4, Mishnah 1. This mishnah deals with the times of the three daily prayers - Shacharis, Minchah and Maariv - as well as the time of the Mussaf prayer.
"Tefillas hashachar ad chatzos":
The Shemoneh Esrei of Shacharis may be recited until midday, the midpoint between sunrise and sunset. This time must be distinguished from the time for Shema, which, as we have mentioned, extends only until three hours into the day.
"Rabbi Yehudah omer ad arba shaos" - Rabbi Yehudah disagrees and holds that the time ends at the conclusion of the fourth hour of the day. The hours used by the mishnah are proportional hours: not an hour of sixty minutes as such, but the division of the time from sunrise to sunset into twelve parts, each such part being one proportional hour. According to Rabbi Yehudah, at the end of four proportional hours the time for reciting the Shemoneh Esrei of Shacharis has passed.
The basis of the dispute: the morning prayer was instituted to correspond to the daily morning Tamid offering that was brought in the Beis HaMikdash, and regarding the time of its offering there was a parallel dispute - whether it could be brought until four hours, or whether the time extended until midday. The halachah is that one may pray until midday, but the concept of 'tefillah bizmanah' - fulfilling the prayer at its proper time - is achieved only by praying within the first four hours, in accordance with Rabbi Yehudah's opinion.
"Tefillas haminchah ad ha'erev":
Minchah may be recited until evening, that is, until sunset. "Rabbi Yehudah omer ad plag haminchah" - until half of the Minchah period. To understand this:
Minchah Gedolah: from six and a half hours into the day (half an hour after midday) - the time from which the afternoon Tamid could be offered.
Minchah Ketanah: from nine and a half hours into the day until sunset - this is the usual time at which the afternoon Tamid, the daily afternoon offering, was brought in the Beis HaMikdash. This is the 'Minchah' to which the mishnah refers.
Plag HaMinchah: half of the Minchah Ketanah period - the midpoint between nine and a half hours and the end of the twelfth hour, which is the end of the day; that is, ten hours and forty-five minutes into the day, according to the reckoning of proportional hours.
"Tefillas ha'erev ein lah kevah":
Maariv has no fixed time, and the entire night is available to the one who prays (although Shema must be recited before midnight). The choice of the phrase "ein lah kevah" rather than "all night" teaches an additional point: the Sages did not establish Maariv with the same level of obligation and responsibility that they established for Shacharis and Minchah, and Maariv is defined as 'optional'. Nevertheless, as the Rambam writes, all of Israel in every place have adopted the practice of praying Maariv, and therefore its status is that of an obligatory prayer in every respect.
"Veshel Mussaf kol hayom":
Mussaf may be recited throughout the entire day. "Rabbi Yehudah omer ad sheva shaos" - in his opinion the time for Mussaf is limited to the end of the seventh hour of the day, one hour after midday.
In summary: in this mishnah we learned the times of the prayers - Shacharis until midday (and according to Rabbi Yehudah until four hours, paralleling the dispute about the time of the morning Tamid), Minchah until evening (and according to Rabbi Yehudah until Plag HaMinchah), Maariv which has no fixed time and was therefore defined as 'optional' even though it has been adopted as an obligation, and Mussaf all day long (and according to Rabbi Yehudah until seven hours).