Understanding the strcmp () function in a single monthly reminder program

Here is a program that prints a list of reminders for one month. This is an example of K.N. King of the book. My problem is that I cannot understand how the strcmp function works in this program.

#include <stdio.h>
#include <string.h>

#define MAX_REMIND 50       /* Maximum number of reminders */
#define MSG_LEN 60          /* max length of reminders message */

int read_line(char str[], int n);

int main(void) {
    char reminders[MAX_REMIND][MSG_LEN+3];
    char day_str[3], msg_str[MSG_LEN+1];
    int day, i, j, num_remind = 0;

    for(;;) {
        if(num_remind == MAX_REMIND) {
            printf("--No space left--\n");
            break;
        }

        printf("Enter day and reminder: ");
        scanf("%2d", &day);
        if(day == 0)
            break;
        sprintf(day_str, "%2d", day);
        read_line(msg_str, MSG_LEN);

        for(i = 0; i < num_remind; i++)
            if(strcmp(day_str, reminders[i]) < 0)
                break;

        for(j = num_remind; j > i; j--) 
            strcpy(reminders[j], reminders[j - 1]);

        strcpy(reminders[i], day_str);
        strcat(reminders[i], msg_str);

        num_remind++;
    }

    printf("\nDay Reminder\n");
    for(i = 0; i < num_remind; i++)
        printf(" %s\n", reminders[i]);

    return 0;
}

int read_line(char str[], int n) {
    int ch, i = 0;
    while((ch = getchar()) != '\n')
        if (i < n)
            str[i++] = ch;

    str[i] =  '\0';
    return i;
}

I realized that the lines are stored in a 2D array in which each line receives a line from the user. The program first accepts the date (in two decimal words from the user) and converts it to a string using the sprintf () function. Then it compares the converted string date with the string stored in the reminder array [] [].

I can't figure out how it compares a date with a string. (It always returns true in this case and is interrupted for the operator at i = 0 each time).